I think you probably mean "You should check your answers carefully." "Check your test paper carefully" is OK, but it is better to be perfectly clear. Check what? Check the answers.
To "check" means "to verify something to make sure it is correct. To "examine" is less definite. It just means "to look at something carefully."
I am going to write three longer passages showing the context in which each phrase could be used.
"After you finish, you should check your answers carefully. Look them over a second time. Make sure you haven't made any careless mistakes."
"Examine your test paper carefully before you turn it in. In addition to checking your answers, make sure that you've answered every question, that all your answers are legible, and that you've written your name on every page."
"Before you begin, please examine your test carefully. You should have four pages, with questions printed on both sides of each page. The questions are numbered from 1 to 50, check to make sure you have them all.